The generator matrix

 1  0  1  1  1  1  1 2X^2  1  1  1  1 2X  1  0  1
 0  1  1  2  0 2X+1 2X^2+2  1 2X^2+2X 2X^2+2X+2 X+1 2X^2+X+2  1 X^2+2X+1  1  0
 0  0 2X  0 X^2  X 2X^2+X X^2+X X^2+X 2X^2+2X 2X^2 X^2  0 2X^2+X  X  0
 0  0  0  X 2X^2+2X 2X^2 X^2+2X 2X 2X^2+2X  X X^2+2X 2X X^2+2X 2X 2X^2+X X^2

generates a code of length 16 over Z3[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+52x^24+114x^25+372x^26+696x^27+1674x^28+1614x^29+7594x^30+7290x^31+14688x^32+14618x^33+6690x^34+2202x^35+1058x^36+252x^37+78x^38+38x^39+18x^40

The gray image is a linear code over GF(3) with n=144, k=10 and d=72.
This code was found by Heurico 1.16 in 1.5 seconds.